Santiago Montenegro, a visiting fellow at the Center of Hemispheric Policy, University of Miami, was Director of Colombia’s National Planning Department (2002-2006) and Dean of the School of Economics, Los Andes University (1996-2000).

What is neither a conservative approach nor disappointing is the use of a quadratic qualia system using a diagram similar to the one familiar in mathematics by Descartes. As might be observed, the opposite of Category A (field A or ++) is Category C (field C or --); the opposite of Category B (field -+) is Category D (field +-).

The use of this system may be demonstrated shortly and sweetly, especially without invoking competition or numbers. Every variable considered is reduced to a category, and must consist of an exclusive quality, defined as a quality that has an opposite. Axis A-C and Axis B-D are then set to be opposites, one (the first) being a subject axis, and the second a context axis.

In one example, Digital-Watch (two variables, which we will treat as not opposite, and hence the basis for two further opposites) reduces to Math-Time. Math-NonMath becomes one axis, and Time-Immortal becomes another axis. Here the possible comparisons are not between opposites, because this would be contradictory, but between non-opposites. However, multiple non-opposites can be combined. The result is two ideas: [1] Immortal Math, Time for Non-Math is one set, and [2] Immortal Non-Math, Time for Math is another set.

This may seem useless at first, until the analogy of the digital watch is introduced. [1] Immortal Math refers to the function of the watch (originally a digital display), suggesting a possibility of more accurate displays, called immortal displays, such as a Subliminal Watch, a Wireless Watch, or a Health Watch, or some combination of these. [2] Non-math is originally a reference to the opposite of the display, but here could mean an opposite category of watch function, such as a Mechanical Watch (a watch that serves as a tool rather than a watch), a Kinetic Watch (a watch with an aesthetic, musical, or game function), or a Self-Winding Watch. [3] Immortal non-math refers originally to the pure opposite of the digital watch, and occurs at stage three to inspire creativity. What might be considered is a watch (the base function) upon which time has operated, instead of one that operates time by itself. In this case, good solutions might be a Time Sculpture, a Screen Saver, or a watch that operates by changing shape or acquiring physical rather than linguistic marks. For example, a watch that appeals to emotions, or a watch that depicts things that happen during that time of day. [4] Time for math returns the categorical puzzle box to the original position, concerned with what the watch already is. Essentially, any of the above-mentioned types of watches and watch functions might be applied to the original design. The key insight is that there is a direct variable-to-variable correlation. For example, if we want to depict storm clouds on the watch on a screen, the storm clouds must relate to one of the two original elements: time or math (the name of this category). For example, the storm clouds could be a number system, or the storm clouds could rain when it is time for an appointment, etc.

I think that clarifies the potential importance of categorical knowledge in inspiring innovation and design. More about this in my book, The Dimensional Philosopher's Toolkit (2013), which explains the method of categorical deduction in detail, with examples of advanced methods and variations.

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